Least Common Multiple (LCM) of 110 and 139
The least common multiple (LCM) of 110 and 139 is 15290.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 110 and 139?
First, calculate the GCD of 110 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 139 = 0 remainder 110 |
| 2 | 139 ÷ 110 = 1 remainder 29 |
| 3 | 110 ÷ 29 = 3 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 34 | 204 |
| 68 and 45 | 3060 |
| 109 and 180 | 19620 |
| 184 and 179 | 32936 |
| 16 and 56 | 112 |